Question Number 207639 by hardmath last updated on 21/May/24
Commented by Berbere last updated on 21/May/24
$${false}\:{not}\:{true}\: \\ $$$$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\sim\frac{\mathrm{4}^{{n}} }{\:\sqrt{\pi{n}}} \\ $$$$\frac{\mathrm{2}^{−\mathrm{2}\left({n}−\mathrm{1}\right)} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right)}{\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)}\begin{pmatrix}{{n}}\\{\mathrm{2}{n}}\end{pmatrix}^{\mathrm{2}} \sim\frac{\mathrm{4}^{{n}} }{\pi{n}}\:{diverge} \\ $$